3D Simulations of Secondary Electron Generation in Diamond and RF Gun Modeling with VORPAL

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3D Simulations of Secondary Electron Generation
in Diamond and RF Gun Modeling with VORPAL
Tech-X Corporation
D. A. Dimitrov
Main contributors D. Bruhwiler, R. Busby, D.
Smithe, P. Messmer, J. R. Cary, Ilan Ben-Zvi, T.
Rao, D. Kayran
Work supported by the US Dept. of Energy.
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Collaborators

• Ilan Ben-Zvi
• T. Rao
• D. Kayran
• J. Smedley
• X. Chang
• Q. Wu
• Brookhaven National Lab

• D. L. Bruhwiler
• R. Busby
• D. Smithe
• P. Messmer
• C. Nieter
• J. R. Cary
• VORPAL developers
• Tech-X Corporation

• J. Lewellen
• Argonne National Lab

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Motivation-I

• A new design for a photoinjector was recently
  proposed using diamond as an amplifier of primary
  electrons.
• The design is very promising for generation of
  high-current, high-brightness electron beam.
• Experiments have demonstrated the viability of
  the concept but the optimal design and parameters
  of operation are still being investigated.
• Realistic PIC simulations of a photoinjector with
  a diamond amplifier are currently not available.
• Such simulations are expected to provide valuable
  guidance when designing these devices.

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Motivation-II

• Generation of high order modes in an SRF electron
  gun with high average and peak current is a
  serious concern.
• Only a fully electromagnetic code can study this
  problem.
• The 3D massively parallel particle-in-cell (PIC)
  code VORPAL is uniquely suited for this
  application.
• Investigate how VORPAL compares with PARMELA to
  model RF gun properties.

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Schematic diagram of a secondary emission
enhanced photoinjector (SEEP) courtesy of
Triveni Rao
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Physical Processes Involved

• Elastic scattering - implemented two models
• Isotropic and small angle scattering more
  accurate model currently considered
• Inelastic scattering for secondary electron and
  hole generation that takes band structure into
  account - implemented
• Electron-hole recombinations
• Acoustic and optical phonon scattering
  (inelastic)
• Scattering from impurities and defects
• Emission from diamond surfaces taking into
  account different electron affinities.

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Total Elastic and Inelastic Scattering Cross
Sections

• mean free time

• mean free path

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Generation of Secondary Electrons and Holes

• General Monte Carlo algorithm implemented for
  scattering processes
• Electrons or holes with Ekin gt EG (5.46 eV) can
  generate secondaries

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PDF for the Primary Electron Momentum Change
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Energy Loss Function
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Sampling from the PDF for the Primary Electron
Momentum Change
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Yield of Secondary Electrons is in Fair Agreement
with Previous Simulations
EC 29 (eV) EG 5.46 (eV)
Ep 1000 EC (eV)
Ep 250 EC (eV)

• Two limiting cases considered
• With energy loss to lattice
• No energy loss to lattice
• Averages for Ne are over 200 runs.

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Yield of Secondary Electrons is in Fair Agreement
with Previous Simulations

• Comparison is not under the same conditions.
• Bejata et al. reported

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VORPAL Geometry Representation Capability

• VORPAL software is able to do curved surfaces
  modeling.
• Improves accuracy of wakefield and HOM coupling
  and propagation through apertures.
• Cavity focusing and defocusing effects during
  acceleration-deceleration passes.

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VORPAL Provides Second Order Accuracy for 3-D
Accelerating Cavities

• Most codes use stair-step (first order accurate)
  boundaries.

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Geometry Representation for the 1.5 Cell RF Gun
Developed in BNL

• 3D VORPAL representation.
• SUPERFISH axially symmetric description.

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Simulation Parameters

• RF field frequency 703.75 MHz
• RF field at cathode surface at t 0 -8.28 MV/m
• RF phase 40 degrees
• RF field amplitude 30 MV/m
• Beer can beam shape with approximately 5 nC total
  charge
• Beam radius 4 mm
• Beam length 80 ps

Ez (MV/m)
z (cm)

• Multi bunch simulations
• Bunches emitted at each RF period
• 3.5 A average current
• Only at lowest grid resolution currently

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VORPAL Average Kinetic Energy Agrees Well with
PARMELA

• Provides confirmation that accelerating RF fields
  are approximately correct.

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Wakefield effects cause less than 1 variation
in Ekin for multi bunch runs
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Comparison of RMS Bunch Length - I

• VORPAL results show shorter bunch length but
  getting close to the PARMELA result when
  increasing the longitudinal grid resolution.

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Comparison of RMS Bunch Length - II

• The behavior is qualitatively similar.

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Multi Bunch Variation in Zrms

• The wakefieds cause variation in the range
• -1 lt Zrmslt 4
• Most beams are shorter than the first beam by 1
• The 8th beam is longer by 4 .

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VORPAL Shows Qualitatively Similar Transverse RMS
Size Behavior

• The observed transverse rms size was smaller in
  VORPAL (the beam was emitted with no thermal
  velocities).

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Wakefield Effects on the Transverse RMS Size

• Consecutive bunches expand transversely by 3
  relative to the first bunch.

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RMS Emittance - I

• Further studies are needed to understand the
  differences in the rms emittance, particularly
  the effect of wake fields included in VORPAL self
  consistently.

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RMS Emittance - II

• At the exit of the gun, VORPAL shows about 3
  times larger emittance. Detailed convergence
  simulation at different parameter sets should
  provide better understanding of the importance of
  different algorithms.

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Multi Bunch Simulations Show Small Emittance
Increase

• On average, the increase at the exit is 4 .
• Emittance varies from -2 to 4 .

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Summary and Future Work

• 3D parallel PIC simulations with VORPAL
  demonstrated that the code is uniquely suited for
  SRF electron gun studies.
• Initial simulations and benchmarking of VORPAL
  results show quantitative agreement with PARMELA
  for some beam parameters and qualitative for
  others.
• Future studies will focus on
• Completing algorithms for
• electron-hole transport in diamond
• emission of electrons from diamond surfaces
• higher accuracy algorithms,
• simulation studies with PML boundary conditions,
• more accurate treatment of RF fields
• investigation of higher order modes

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Acknowledgments
This work was supported by the US Department of
Energy, office of Nuclear Physics, under an SBIR
grant and Tech-X Corp.
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